Lloyd's original work considered the simulation of \(k\) -local Hamiltonians. This was subsequently extended to the study of \(d\) -sparse Hamiltonians [1]}, [2]}, which provides a framework that abstracts the design of quantum algorithms from the underlying physical settings. However, despite their theoretical value, algorithms for sparse Hamiltonian simulation do not always provide the fastest approach for simulating concrete physical systems. Hamiltonians arising in practice often have additional features beyond sparseness, such as locality [3]}, [4]}, commutativity [5]}, [6]}, [7]}, and symmetry [8]}, [9]}, that can be used to improve the performance of simulation. Besides, prior knowledge of the initial state [10]}, [11]}, [12]}, [13]} and the norm distribution of Hamiltonian terms [14]}, [15]}, [16]}, [17]}, [18]} have also been proven useful for digital quantum simulation.
